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BEST PROXIMITY POINT THEOREMS FOR CYCLIC QUASI-CONTRACTION MAPS IN UNIFORMLY CONVEX BANACH SPACES

Part of: Spaces with richer structures Connections with other structures, applications Nonlinear operators and their properties

Published online by Cambridge University Press:  13 October 2016

NGUYEN VAN DUNG  and
VO THI LE HANG
NGUYEN VAN DUNG*
Affiliation:
Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam email [email protected]
VO THI LE HANG
Affiliation:
Faculty of Mathematics and Information Technology Teacher Education, Dong Thap University, 783 Pham Huu Lau Street, Ward 6, Cao Lanh City, Dong Thap Province, Viet Nam email [email protected]
*
✉ [email protected]
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Abstract

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In this paper we first give a negative answer to a question of Amini-Harandi [‘Best proximity point theorems for cyclic strongly quasi-contraction mappings’, J. Global Optim.56 (2013), 1667–1674] on a best proximity point theorem for cyclic quasi-contraction maps. Then we prove some new results on best proximity point theorems that show that results of Amini-Harandi for cyclic strongly quasi-contractions are true under weaker assumptions.

Keywords

cyclic quasi-contractionbest proximity pointuniformly convex Banach space

MSC classification

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
Secondary: 54E05: Proximity structures and generalizations 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 1 , February 2017 , pp. 149 - 156
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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